The Meaning of

Interior Tomography

Ge Wang, PhD, Director

SBES Division & ICTAS Center for Biomedical Imaging

VT-WFU School of Biomedical Engineering & Sciences

Virginia Tech, Blacksburg, VA, USA

ge-wang@ieee.org

October 1, 2010

Interior Tomography (2007)

Object

BeamSour

ceTrajectory

ROI

Object

Beam

Trajectory

ROI

Object

Beam

Trajectory

Known

Sub-region

ROI

Object

Beam

Trajectory

Sparsity

Model

Regular Reconstruction Interior Problem

Landmark-based

Interior Tomography

Sparsity-based

Interior Tomography

First Paper (May 2007)

Independent Work (Oct. 2007)

Interior CT Patent

Literature Analysis

Outline

• Less Is Deeper

• Less Is Larger

• Less Is Faster

• Less Is Less

• Less Is More

Less Is Deeper

Use of less projection data for accurate image reconstruction demands

deeper insight, more advanced theory and more powerful tools.

Computed Tomography (Wholesale)

t

Sinogram

X-rays

Projectio

n:

Linear in

tegral

s

t

y

x

p

Measurement

Reconstruction

Object),( yxf

),( tP

Inner Vision with Local Data (Retail)

t

Sinogram

X-rays

Projectio

n:

Linear in

tegral

s

ty

x

Measurement

Reconstruction

Object),( yxf

),( tP

X X

Earliest BPF Formula (1991)

Half-PI-Line Reconstruction (2006)

Field of View (FOV)

Partial-PI-Line

Extrapolation from a Known Point (2006)

FOV

?

Curved Filtering Path (2003)

?

Interior Reconstruction

(a) (b)

50 100 150 200-1000

-500

0

500

(HU)

(Pixel)

(c)

50 100 150 200-1000

-500

0

500

(HU)

(Pixel)

(d)

Global

FBP

Local

FBP

Local

SART

Interior

Recon

HOT

Sparsity-based Interior Recon

Outline

• Less Is Deeper

• Less Is Larger

• Less Is Faster

• Less Is Less

• Less Is More

Less Is Larger

Acquisition of less projection data is achieved with a narrower beam, and

an object larger than the beam width is not a concern.

Preclinical Nano-CT

X-ray Beam Central Stop

Condense Lens

Sample

Zone

Plate

Phase Ring

Detector Plane

Rot

atio

n A

xis

ROI

Sample Stage

Potential for Study on Earliest Life

Hagadorn JW, et al. (2006) Cellular and subcellular structure of Neoproterozoic embryos.

Science 314:291–294

Big Patient Problem

Outline

• Less Is Deeper

• Less Is Larger

• Less Is Faster

• Less Is Less

• Less Is More

Less Is Faster

Less data means smaller detector size, faster frame rate, and more imaging

chains, all of which contribute to accelerate the data acquisition process.

Spiral Cone-beam CT

Dual-source Clinical CT (2005)

Multi-source Interior Tomography

X-ray Detectors

X-ray Tubes

ROI

Wang G, Yu H, Ye YB. Virginia Tech Patent Disclosure on May 15, 2007,

US Patent Application 12/362,979 allowed on October 21, 2009

Ye YB, Yu HY, Wei YC, Wang G. International Journal of Biomedical Imaging, Article ID:63634, 2007

Wang G, Yu H, Ye Y. Medical Physics. 36:3575-3581, 2009

From Scanning to Roaming

Outline

• Less Is Deeper

• Less Is Larger

• Less Is Faster

• Less Is Less

• Less Is More

Less Is Less

Less data is equivalent to less radiation dose, because of not only a

narrower beam but also a more relaxed angular sampling requirement in

the longitudinal studies or multi-scale scenarios.

Reduced Angular Sampling Rate

Need 2 ProjectionsNeed 4 Projections

Statistical Interior Tomography

Work in progress from Qiong Xu & Xuanqin Mou (China) in collaboration with Wang G

& Yu HY

Phantom [0.9 1.1]

ROI

Hilbert Region

Known sub-Region20

0,00

0 ph

oton

s50

,000

pho

tons

ITHT ML

Outline

• Less Is Deeper

• Less Is Larger

• Less Is Faster

• Less Is Less

• Less Is More

Less Is More

Use of less data is advantageous in more modalities beyond CT, such as

other straight-ray tomographic techniques and even in small-angle

curvilinear geometry, and more applications of various types.

Furthermore, less data means more computational time!

Interior-MRI

……………………………………

Interior-MRI

Zhang J, Yu HY, Corum C, Garwood M, Wang G: Exact and stable interior ROI reconstruction for radial MRI. SPIE 7258: 2585G,

8 pages, Feb. 2009, Orlando, FL, USA

Traditional MRI Interior MRI

Interior Electron Tomography

Ge Wang, Hengyong Yu

Limited Angle Interior Tomography

Interior SPECT

Interior-SPECT

Support

FOVK

now

n Idea

l dat

a

Yu HY, Yang JS, Jiang M, Wang G: Interior SPECT- Exact and stable

ROI reconstruction from uniformly attenuated local projections;

Communications in Numerical Methods in Engineering, 25(6):693-710,

2009

µa =0cm-1

µa =0.15cm-1

µa =0.3cm-1

Noi

sy d

ata

Practical Implications

Conclusion

• Less Is Deeper

• Less Is Larger

• Less Is Faster

• Less Is Less

• Less Is More

Less Is Not Always Better

Link of Localities

Pictures from http://www.bing.com

• Multi-scale Interior Tomography

• Multi-parameter Interior Tomography

• Multi-energy Interior Tomography

Future Work

SBES Advanced Multi-scale CT Facility

Smaller Scales?

Larger Scales?

Multi-parameter CT

Grating-based Imaging

Wang G, Cong W, Shen H, Zou Y: Varying Collimation for Dark-Field Extraction. International Journal of

Biomedical Imaging. 2009, Article ID 847537, 2010

Dark-field Tomography

Multi-energy CT

• Theoretical Extension

• Computational Optimization

• Systematic Evaluation

• Biomedical Applications

• Interdisciplinary Collaboration

Future Work

Acknowledgment

The results in this presentation are of collaborative nature. Major collaborators include Drs. Hengyong

Yu, Yangbo Ye, Jiangsheng Yang, Ming Jiang, Steve Wang, Michael Fesser, Erik Ritman, Deepak

Bharkhada, Bruno DeMan, Guohua Cao, Otto Zhou, Alexander Katsevich, et al. The work was

partially supported by National Institutes of Health/National Institute of Biomedical Imaging and

Bioengineering Grants EB002667, EB009275, and EB011785 as well as National Science

Foundation NSF/CMMI 0923297.

Thank You!